Information processing apparatus, information processing system, information processing method, and computer program product

ABSTRACT

According to an embodiment, an information processing apparatus is configured to set a candidate for a time lag until analysis target data including at least one of a measurement item and a setting item for use in control of a process controller affects an objective variable, and a time-lag number allowed in a regression model; select, as a candidate for an explanatory variable, at least one of the measurement item measured at a time corresponding to the candidate for the time lag and the setting item set at the time; and determine a regularization parameter of the regression model such that a number of the time lag is equal to or less than the time-lag number, based on a regularization path indicating transition of a regression coefficient for the candidate for the explanatory variable, the regression coefficient varying in accordance with a value of the regularization parameter.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromJapanese Patent Application No. 2020-154629, filed on Sep. 15, 2020; theentire contents of which are incorporated herein by reference.

FIELD

An embodiment described herein relates generally to an informationprocessing apparatus, an information processing system, an informationprocessing method, and a computer program product.

BACKGROUND

In plant management, it has been widely performed that a regressionmodel that predicts a difficult-to-measure process variable from sensordata of the plant is constructed and a soft sensor that monitors thepredicted value based on the regression model instead of thedifficult-measure process variable. For example, there has beenconventionally known a technique in which automatic extraction of alarge amount of features is performed with a penalized regression modelto construct a regression model.

With such a conventional technique, however, it has been difficult tocontrol the number of time lags associated with each piece of analysistarget data, when constructing a regression model that predicts aprocess variable.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of an exemplary hardware configuration of aninformation processing system of an embodiment;

FIG. 2 is a diagram of an exemplary functional configuration of aninformation processing apparatus of the embodiment;

FIG. 3 is a flowchart of an exemplary information processing methodperformed by the information processing apparatus of the embodiment;

FIG. 4 is a graph of exemplary regularization paths of the embodiment;and

FIG. 5 illustrates exemplary display information of the embodiment.

DETAILED DESCRIPTION

According to an embodiment, an information processing apparatus includesa setting unit, a selection unit, and a determination unit. The settingunit is configured to set a candidate for a time lag until analysistarget data including at least one of a measurement item measured by asensor and a setting item for use in control of a process controlleraffects an objective variable, and a time-lag number allowed in aregression model that predicts the objective variable. The selectionunit is configured to select, as a candidate for an explanatoryvariable, at least one of the measurement item measured at a timecorresponding to the candidate for the time lag and the setting item setat the time. The determination unit is configured to determine aregularization parameter of the regression model such that a number ofthe time lag is equal to or less than the time-lag number, based on aregularization path indicating transition of a regression coefficientfor the candidate for the explanatory variable, the regressioncoefficient varying in accordance with a value of the regularizationparameter, and determine the regression model using the determinedregression parameter.

An embodiment of an information processing apparatus, an informationprocessing system, an information processing method, and a program willbe described in detail with reference to the accompanying drawings.

Exemplary Hardware Configuration

FIG. 1 is a diagram of an exemplary hardware configuration of aninformation processing system 1 of the embodiment. The informationprocessing system 1 of the embodiment is a system for managing a plant.The information processing system 1 of the embodiment includes a processcalculator 2, a process controller 3, an electric motor 4 a, a drivedevice 4 b, a process sensor 5, an operator terminal 6, an informationlocal area network (LAN) 7, a control LAN 8, a management apparatus 9,and an information processing apparatus 15.

The process calculator 2, the process controller 3, the electric motor 4a, the drive device 4 b, the process sensor 5, and the operator terminal6 are connected to the management apparatus 9 via the information LAN 7and the control LAN 8.

For example, the management apparatus 9 collects time-series data fromthe process calculator 2, the process controller 3, and the processsensor 5 via the information LAN 7, and accumulates the time-series datain the management apparatus 9. The time-series data collected from theprocess calculator 2 is, for example, manufacturing information relatedto a plant, and quality information and production information outputeach time a product is manufactured in the plant.

The manufacturing information is information related to a control targetto be used in manufacturing a product. For example, when the controltarget is a valve, the manufacturing information includes the controltarget value of the valve, the information indicating the operation ofthe valve, the observed value according to the operation of the valve,and the like. The quality information indicates the quality of amanufactured product. The production information includes informationsuch as the production volume of the product.

The time-series data collected from the process controller 3 is, forexample, a setting value for use in control of the process controller 3.The time-series data collected from the process sensor 5 is, forexample, a measurement value. The process sensor 5 is, for example, apressure sensor, a fluid sensor, a temperature sensor, or the like.

In addition, the management apparatus 9 collects control informationrelated to process control from the process controller 3 via the controlLAN 8 and accumulates the control information in the managementapparatus 9.

The process controller 3, the electric motor 4 a, the drive device 4,and the process sensor 5 each transmit and receive control informationvia the control LAN 8.

The operator terminal 6, for example, sets and operates the processcontroller 3 via the information LAN 7 and the control LAN 8.

The management apparatus 9 includes a central processing unit (CPU) 10,a random access memory (RAM) 11, a recording medium 12, a communicationinterface 13, and a user interface 14. The CPU 10 is connected to theRAM 11, the recording medium 12, the communication interface 13, and theuser interface 14 via a bus, and controls the RAM 11, the recordingmedium 12, the communication interface 13, and the user interface 14.Furthermore, the CPU 10 sequentially executes computer programs storedin the recording medium 12.

The RAM 11 include a static random access memory (SRAM), a dynamicrandom access memory (DRAM), a flash memory, and the like. In executionby the CPU 10, the RAM 11 reads a computer program or the like stored inthe recording medium 12 as needed, and temporarily stores the computerprogram or the like.

The recording medium 12 includes a hard disk drive (HDD), a solid statedrive (SSD), and the like. The recording medium 12 stores a computerprogram for accumulating the above time-series data in a database andthe database for storing the time-series data.

The communication interface 13 is an interface for connecting to theinformation LAN 7, the control LAN 8, and the information processingapparatus 15.

The user interface 14 includes a display, a keyboard, a mouse, and thelike. The user interface 14 accepts input from the user and outputsinformation.

The information processing apparatus 15 includes a CPU 16, RAM 17, arecording medium 18, a user interface 19, and a communication interface20. The CPU 16 is connected to the RAM 17, the recording medium 18, theuser interface 19, and the communication interface 20 via a bus, andcontrols the RAM 17, the recording medium 18, the user interface 19, andthe communication interface 20. Furthermore, the CPU 16 sequentiallyexecutes computer programs stored in the recording medium 18.

The recording medium 18 includes an HDD, an SSD, and the like. Therecording medium 18 stores a measurement value obtained from the processsensor 5, and a computer program for calculating the magnitude of timedelay (time lag) at the time when the setting value or the like of theprocess controller 3 is recorded, in comparison with the time whenquality information or production information transmitted from theprocess calculator 2 is recorded. In addition, the recording medium 18also stores a computer program for extracting the measurement value fromthe process sensor 5 that contributes to fluctuations in the qualityinformation, the production information, and the like transmitted fromthe process calculator 2. Furthermore, the recording medium 18 stores acomputer program for extracting the setting value of the processcontroller 3 that contributes to the fluctuation of the qualityinformation, the production information, and the like transmitted fromthe process calculator 2.

The RAM 17 include an SRAM, a DRAM, a flash memory, and the like. Inexecution by the CPU 16, the RAM 17 reads a computer program or the likestored in the recording medium 18 as needed, and temporarily stores thecomputer program or the like.

The user interface 19 includes a display, a keyboard, a mouse, and thelike. The user interface 19 accepts input from the user and outputsinformation. The output information is, for example, the above time lag;and the measurement value that contributes to fluctuations of thequality information, the production information, and the like, and thesetting value transmitted from the process calculator 2.

The communication interface 20 is an interface for connecting to theinformation LAN 7, the control LAN 8, and the management apparatus 9.

Exemplary Functional Configuration

FIG. 2 is a diagram of an exemplary functional configuration of theinformation processing apparatus 15 of the embodiment. The informationprocessing apparatus 15 of the embodiment includes a setting unit 31, anacquisition unit 32, a selection unit 33, a calculation unit 34, adetermination unit 35, an evaluation unit 36, and a display control unit37. The setting unit 31, the acquisition unit 32, the selection unit 33,the calculation unit 34, the determination unit 35, the evaluation unit36, and the display control unit 37 are achieved by, for example, acomputer program read from the recording medium 18 to the RAM 17. Inaddition, an analysis-target-data storage unit D1 and atime-lag-group-data storage unit D2 are achieved by the RAM 17 and therecording medium 18.

Exemplary Information Processing Method

FIG. 3 is a flowchart of an exemplary information processing methodperformed by the information processing apparatus 15. First, the settingunit 31 sets parameters input via the user interface 19 (Step S1). Theparameters input via the user interface 19 are an analysis-targetsetting parameter, an analysis-target-period setting parameter, atime-lag-candidate setting parameter, a regularization-candidate settingparameter, a time-lag-number setting parameter, an evaluation-targetsetting parameter, and the like.

The analysis-target setting parameter is a parameter for settinganalysis target data including one or more analysis items. The analysisitems include at least one of a measurement item measured by the processsensor 5 and a setting item for use in the control of the processcontroller 3. In the case of a measurement item, a measurement value ofthe process sensor 5 that measures the measurement item is to beanalyzed. Note that the number of measurement items to be set asanalysis target data may be selected freely. In the case of a settingitem, a setting value of the process controller 3 in which the settingitem is set is to be analyzed. Note that the number of setting items tobe set as analysis target data may be selected freely. Theanalysis-target-period setting parameter is a parameter for setting theanalysis (learning) target period of the analysis target data.

The time-lag-candidate setting parameter includes the unit of the timelag to be considered in the analysis and the maximum value of the timelag. The unit of the time lag to be considered in the analysis is, forexample, 30 min. In addition, the maximum value of the time lag is, forexample, 360 min. In this case, it means to consider the possibleoccurrence of time delay by, such as 30 min, 60 min, 90 min, . . . , and360 min.

The regularization-candidate setting parameter is a parameter forsetting a candidate for a regularization parameter. The candidate forthe regularization parameter may be a discrete value within apredetermined range of values or a continuous value. For regularizationof a regression model, for example, methods such as L1 regularization,smoothly clipped absolute derivation (SCAD), and minimax concave penalty(MCP) are used.

The time-lag-number setting parameter is a parameter for setting thetime-lag number allowed in the regression model that predicts anobjective variable. For example, if at most one time lag is allowed foreach explanatory variable (for example, measurement value and settingvalue), the time-lag number is set to 1.

The evaluation-target setting parameter is a parameter for setting theevaluation target period of the regression model.

Next, the acquisition unit 32 acquires, as analysis target data, datathat matches the analysis-target setting parameter and theanalysis-target-period setting parameter, from the time series dataaccumulated in the management apparatus 9, and then stores the analysistarget data in the analysis-target-data storage unit D1 (Step S2). Notethat the acquisition unit 32 may perform a processing process on theacquired analysis target data. For example, when the analysis targetdata includes a measurement value, the processing process includesremoval of noise included in the measurement value, smoothing of themeasure value, interpolation based on the moving average of themeasurement value, and the like.

Next, the selection unit 33 selects, as time-lag-group data indicating acandidate for the explanatory variable, at least one of the measurementitem measured at the time corresponding to each candidate for a time lagand the setting item set at the time, and then stores the selectedtime-lag-group data in the time-lag-group-data storage unit D2 (StepS3).

Specifically, for example, when the analysis target data is ameasurement value measured for the K number of measurement itemsmeasured by the process sensor 5 and the candidates for the time lag are30 min, 60 min, and 90 min, the selection unit 33 selects thetime-series data m_(t,1), m_(t,2), . . . , m_(t,k) of the measurementitem of time t with no time lag; the time-series data m_(t-30),m_(t-30), . . . , m_(t-30,K) of the measurement item measured 30 minbefore; the time-series data m_(t-60,1), m_(t-60,2), . . . , m_(t-60,K)of the measurement item measured 60 min before; and the time-series datam_(t-90,1), m_(t-90,2), . . . , m_(t-90,K) of the measurement itemmeasured 90 min before. Note that time t is a variable representing thetime included in the analysis target period. The time-lag-group data attime t in this case is a set of candidates for the explanatory variable(m_(t,1), m_(t,2), . . . , m_(t,K), m_(t-30), m_(t-30,2), . . . ,m_(t-30,K), m_(t-60,1), m_(t-60,2), . . . , m_(t-60,K), m_(t-90,1),m_(t-90,2), . . . , m_(t-90,K)).

In addition, for example, when the analysis target data is a settingvalue set for the J number of setting items set in the processcontroller 3 and the candidates for the time lag are 60 min and 120 min,the selection unit 33 selects the time-series data s_(t,1), s_(t,2), . .. , s_(t,J) of the setting item of time t with no time lag; thetime-series data s_(t-60,1), s_(t-60,2), . . . , s_(t-60,J) of thesetting item set 60 min before; and the time-series data s_(t-120,1),s_(t-120,2), . . . , s_(t-120,J) of the measurement item set 120 minbefore. The time-lag-group data at time t in this case is a set ofcandidates for the explanatory variable (s_(t,1), s_(t,2), . . . ,s_(t,J), s_(t-60,1), s_(t-60,2), . . . , s_(t-60,J), . . . , s_(t,J),s_(t-120,1), s_(t-120,2), . . . , s_(t-120,J)).

For the unit of the time lag and the maximum value of the time lag, adefault value may be used, instead of setting in the processing of StepS1.

The calculation unit 34 reads the time-lag-group data stored in thetime-lag-group-data storage unit D2, and calculates, for each analysisitem (measurement item or setting item), a regularization pathindicating the transition of the regression coefficient for thecandidate for the explanatory variable that varies in accordance withthe value of the regularization parameter of the regression model (StepS4). The calculation unit 34 calculates such a regularization path byusing, for example, a penalized regression with L1 regularization.

Exemplary Regularization Path

FIG. 4 is a graph of exemplary regularization paths of the embodiment. λon the horizontal axis represents the value of a regularizationparameter, and β on the vertical axis represents a regressioncoefficient. Each break line indicates a regularization pathcorresponding to candidates for an explanatory variable (for example,one measurement item of the process sensor 5 or one setting item of theprocess controller 3) of a penalized regression model that predicts anobjective variable (for example, quality information and productioninformation). For example, in the case of a regularization path for ameasurement value indicating temperature that is one of the measurementitems, each break line corresponds to the measurement value of thetemperature in consideration of a different time lag. The data to beused for calculating the regularization path is acquired by theacquisition unit 32, based on the analysis-target setting parameter andthe analysis-target-period setting parameter above. A candidate for theregularization parameter may be given based on the aboveregularization-candidate setting parameter, or a default value mayalways be used. Graphs indicating such regularization paths will beobtained for the number of measurement items or the number of settingitems.

Based on the number of measurement items or the number of setting items,and the acquired regularization paths, the determination unit 35determines regularization parameters λ for the number of measurementitems or the number of setting items such that the number of time lagsare the time-lag number set by the setting unit 31 (for example, 1) orless. For example, when the time-lag number set by the setting unit 31is 1, the regularization parameters λ are determined to be values nearthe vertical line 102. Note that the regression coefficient β of thebreak line 101 a is always 0, and thus the measurement item or thesetting item having the time lag corresponding to the break line 101 ais excluded from the explanatory variable of the penalized regressionmodel. In a case where the regularization parameters λ are determined tobe values value near the vertical line 102, the time lag of themeasurement item or the setting item corresponding to thisregularization path is determined to be the time lag corresponding tothe regularization path indicated by the break line 101 b.

Furthermore, for example, when the time-lag number set by the settingunit 31 is 2, the regularization parameters λ are determined to bevalues near the vertical line 103.

Referring back to FIG. 3, the determination unit 35 then receives theregularization parameter list D3 and the regression coefficient D4according to the regularization parameter list D3 from the calculationunit 34, and accepts the above time-lag-number setting parameter fromthe setting unit 31. Then, the determination unit 35 determines aregularization parameter λ for each analysis item (measurement item orsetting item) from the regularization parameter list D3 such that thenumber of time lags is the time-lag number (for example, 1) set with thetime-lag-number setting parameter, newly sets the maximum value of theregularization parameters λ as a regularization parameter, and thendetermines the regression model D5 (penalized regression model) (StepS6).

Next, based on the above evaluation-target setting parameter, theevaluation unit 36 reads the time-lag-group data from thetime-lag-group-data storage unit D2, evaluate the performance of theregression model (D5) with the time-lag-group data, and then calculatesthe model accuracy (D6) such as a determination coefficient (R²) or amean squared error (MSE) (Step S6). Particularly, the evaluation unit 36specifies the evaluation target period of the regression model (D5) fromthe evaluation-target setting parameter, and uses, among the pieces oftime-series data included in the time-lag-group data, the time-seriesdata according to the time lag to be evaluated, for evaluation of theregression model (D5).

Next, the display control unit 37 accepts the regression model D5 andthe model accuracy D6, and then displays display information based onthe regression model D5 and the model accuracy D6 on the user interface19 (Step S7). The display information includes, for example, theobjective variable, the explanatory variable of the regression model D5,and the time lag based on the regularization parameter used for thedetermination of the regression model D5.

Exemplary Display Information

FIG. 5 illustrates exemplary display information of the embodiment. Eachdisplay 111 indicates the time lag of an explanatory variable. For anexplanatory variable (for example, measurement item of the processsensor 5 and setting item of the process controller 3) that affects anobjective variable (for example, quality information and productioninformation) without time delay, the time lag is displayed as, forexample, 0 h. Each graph 112 indicates the time-series data of thevalues of the explanatory variable. The graph 112 is displayed bysliding in accordance with the time lag indicated on the display 111.The graph 113 indicates the time-series data of the values of anobjective variable. As in the example of FIG. 5, the measurement valueof the process sensor 5 that does not affect the objective variable (forexample, quality information and production information) and the settingvalue of the process controller 3 are not displayed, so that fluctuationfactors for the objective variable can be confirmed more efficiently.

As described above, in the information processing apparatus 15 of theembodiment, the setting unit 31 sets the candidates (for example, 0 h, 1h, . . . , 6 h) for the time lag until the analysis target dataincluding at least one of the measurement item measured by the processsensor 5 and the setting item for use in the control of the processcontroller 3, and the time-lag number allowed in the regression model D5that predicts the objective variable. The selection unit 33 selects, asthe candidate for the explanatory variable, at least one of themeasurement item measured at the time corresponding to the candidate forthe time lag and the setting item set at the time. Then, based on theregularization path indicating the transition of the regressioncoefficient D4 for the candidate for the explanatory variable thatvaries in accordance with the value of the regularization parameter ofthe regression model D5, the determination unit 35 determines theregularization parameter λ such that the number of time lags are thetime-lag number set by the setting unit or less, and then determines theregression model D5 with the determined regression parameter λ.

Thus, according to the information processing apparatus 15 of theembodiment, when constructing a regression model that predicts a processvariable, there can be controlled the number of time lags associatedwith each piece of analysis target data. Specifically, for example, inplant management, when a physical unknown fixed time lag is presentbetween the measurement time point of a process variable that isdifficult to be measured and the measurement time point of the sensor tobe used for prediction of the process variable, calculated can be theregression coefficient for the explanatory variable with the expectabletime lag delayed for the regularization parameter list D3. Setting, inadvance, the time-lag number allowed in the regression model D5 to 1enables to select exactly one suitable time lag for each process sensor5 without selecting a plurality of time lags for the same process sensor5, for example.

Note that the functions of the information processing apparatus 15 ofthe embodiment may be achieved by a program (software).

A program that is executed by a computer is recorded in acomputer-readable storage medium such as a CD-ROM, a memory card, aCD-R, or a digital versatile disc (DVD) in an installable or executableformat file, and is provided as a computer program product.

Alternatively, the program that is executed by the computer may bestored on the computer connected to a network such as the Internet, andmay be provided by being downloaded via the network. Alternatively, theprogram that is executed by the computer may be provided via a networksuch as the Internet, without being downloaded.

Alternatively, the program that is executed by the computer may beincorporated in a ROM or the like in advance and the incorporatedprogram may be provided.

The program that is executed by the computer has a module configurationincluding a functional block achievable by the program among thefunctional configurations (functional blocks) of the above informationprocessing apparatus 15. As practical hardware, each of the functionalblocks is loaded on the RAM 17 by the CPU 16 reading the program fromthe storage medium and executing the program.

Note that each of the above functional blocks may be achieved byhardware such as an integrated circuit (IC), without being achieved bysoftware.

When each function is achieved with a plurality of processors, eachprocessor may achieve one of the functions, or may achieve two or moreof the functions.

In addition, the operation mode of the computer that achieves theinformation processing apparatus 15 may be selected freely. For example,the information processing apparatus 15 may be achieved by one computer.Furthermore, for example, the information processing apparatus 15 may beoperated as a cloud system on a network.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiment described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the inventions.

What is claimed is:
 1. An information processing apparatus comprising: amemory; and one or more hardware processors electrically coupled to thememory and configured to function as: a setting unit configured to set acandidate for a time lag until analysis target data including at leastone of a measurement item measured by a sensor and a setting item foruse in control of a process controller affects an objective variable,and a time-lag number allowed in a regression model that predicts theobjective variable; a selection unit configured to select, as acandidate for an explanatory variable, at least one of the measurementitem measured at a time corresponding to the candidate for the time lagand the setting item set at the time; and a determination unitconfigured to determine a regularization parameter of the regressionmodel such that a number of the time lag is equal to or less than thetime-lag number, based on a regularization path indicating transition ofa regression coefficient for the candidate for the explanatory variable,the regression coefficient varying in accordance with a value of theregularization parameter, and determine the regression model using thedetermined regression parameter.
 2. The apparatus according to claim 1,wherein the measurement item includes a plurality of measurement items,the setting item includes a plurality of setting items, the analysistarget data includes, as a plurality of analysis items, at least eitherthe plurality of measurement items or the plurality of setting items,and the determination unit is configured to determine, based on theregularization path, the regularization parameter such that the numberof the time lag is equal to or less than the time-lag number, for eachof the plurality of analysis items, and determine the regression modelusing the determined regularization parameter.
 3. The apparatusaccording to claim 1, wherein the setting unit is configured to set aplurality of candidates as the candidate for the time lag, and sets thetime-lag number to
 1. 4. The apparatus according to claim 1, wherein thehardware processors are further configured to function as: a displaycontrol unit configured to display, on a display unit, displayinformation including the objective variable, the explanatory variableof the regression model, and the time lag based on the regularizationparameter used to determine the regression model.
 5. The apparatusaccording to claim 1, wherein the hardware processors are furtherconfigured to function as: a calculation unit configured to calculatethe regularization path.
 6. The apparatus according to claim 5, whereinthe calculation unit is configured to calculate the regularization pathusing a penalized regression with L1 regularization.
 7. The apparatusaccording to claim 5, wherein the calculation unit is configured toselect a value of the regularization parameter from a regularizationparameter list including a plurality of regularization parameters. 8.The apparatus according to claim 1, wherein the hardware processors arefurther configured to function as: an acquisition unit configured toacquire the analysis target data.
 9. The apparatus according to claim 8,wherein the analysis target data includes the measurement item, and theacquisition unit is configured to perform, on the acquired measurementitem, a processing process including at least one of removal of noiseincluded in the measurement item, smoothing of the measurement item, andinterpolation based on a moving average of the measurement item.
 10. Aninformation processing system comprising: a sensor configured to measurea measurement value of a measurement item; a setting unit configured toset a candidate for a time lag until analysis target data including atleast one of the measurement item and a setting item for use in controlof a process controller affects an objective variable, and a time-lagnumber allowed in a regression model that predicts the objectivevariable; a selection unit configured to select, as a candidate for anexplanatory variable, at least one of the measurement item measured at atime corresponding to the candidate for the time lag and the settingitem set at the time; and a determination unit configured to determine aregularization parameter of the regression model such that a number ofthe time lag is equal to or less than the time-lag number, based on aregularization path indicating transition of a regression coefficientfor the candidate for the explanatory variable, the regressioncoefficient varying in accordance with a value of the regularizationparameter, and determine the regression model using the determinedregression parameter.
 11. An information processing method comprising:setting, by an information processing apparatus, a candidate for a timelag until analysis target data including at least one of a measurementitem measured by a sensor and a setting item for use in control of aprocess controller affects an objective variable, and a time-lag numberallowed in a regression model that predicts the objective variable;selecting, by the information processing apparatus, as a candidate foran explanatory variable, at least one of the measurement item measuredat a time corresponding to the candidate for the time lag and thesetting item set at the time; and determining, by the informationprocessing apparatus, a regularization parameter of the regression modelsuch that a number of the time lag is equal to or less than the time-lagnumber, based on a regularization path indicating transition of aregression coefficient for the candidate for the explanatory variable,the regression coefficient varying in accordance with a value of theregularization parameter, and determining the regression model using thedetermined regression parameter.
 12. A computer program productcomprising a non-transitory computer readable medium includingprogrammed instructions, the instructions causing a computer to functionas: a setting unit configured to set a candidate for a time lag untilanalysis target data including at least one of a measurement itemmeasured by a sensor and a setting item for use in control of a processcontroller affects an objective variable, and a time-lag number allowedin a regression model that predicts the objective variable; a selectionunit configured to select, as a candidate for an explanatory variable,at least one of the measurement item measured at a time corresponding tothe candidate for the time lag and the setting item set at the time; anda determination unit configured to determine a regularization parameterof the regression model such that a number of the time lag is equal toor less than the time-lag number, based on a regularization pathindicating transition of a regression coefficient for the candidate forthe explanatory variable, the regression coefficient varying inaccordance with a value of the regularization parameter, and determinethe regression model using the determined regression parameter.